Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-6y &= -3 \\ -7x-6y &= -3\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-7x = 6y-3$ Divide both sides by $-7$ to isolate $x$ $x = {-\dfrac{6}{7}y + \dfrac{3}{7}}$ Substitute this expression for $x$ in the first equation. $-({-\dfrac{6}{7}y + \dfrac{3}{7}}) - 6y = -3$ $\dfrac{6}{7}y - \dfrac{3}{7} - 6y = -3$ Simplify by combining terms, then solve for $y$ $-\dfrac{36}{7}y - \dfrac{3}{7} = -3$ $-\dfrac{36}{7}y = -\dfrac{18}{7}$ $y = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $y$ in the top equation. $-x-6( \dfrac{1}{2}) = -3$ $-x-3 = -3$ $-x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = \dfrac{1}{2}$.